Place the apples with the water in a large, heavy pot. Bring the apples to a simmer over medium-high heat. Reduce the heat, cover the pan, and simmer the apples until they are very tender and starting to fall apart, about 20 minutes (some apples will take longer than others). Stir the apples frequently as they cook to prevent sticking and burning. Add the sugar and stir until dissolved. Add the lemon juice and cinnamon, and stir to combine well.
You can either mash the cooked apples with a wooden spoon against the side of the pot until the mixture is fairly smooth with little chunks of apple, or run the applesauce through a food mill or ricer, which will make it smooth. Taste and adjust the amount of cinnamon and sugar as desired.
Allow to cool to room temperature and transfer to clean dry glass jars.
Seal the jars and refrigerate for up to 3 weeks.
Notes
Good apples for applesauce: Fuji, Gala, Honeycrisp, Golden Delicious, McIntosh, Macouns, Cortland, Gravenstein, Braeburn, Pink LadyVariations:
Unsweetened Applesauce: If you want to skip the sugar altogether, you will have a very soft, natural-tasting applesauce. Sometimes this is desirable when you are serving it with savory food, like pork chops, or if you are looking to cut back on added sugar in your diet.
Applesauce with Cinnamon Candies: This is a very old-school addition, but for many years many cooks added a few tablespoons of those tiny cinnamon candies (sometimes round, sometimes heart-shaped, perhaps called Cinnamon Imperials) to their applesauce. These candies provide sweetness and cinnamon spiciness. You can add them if you like — they also add a notable pinkish hue to the sauce, no matter what kind of apples you choose.